English Translation of Poisson's "Recherches sur la probabilit\'e des jugements en mati\`ere criminelle et en mati\`ere civile" / "Researches into the Probabilities of Judgements in Criminal and Civil Cases"

TL;DR

This paper provides an English translation of Poisson's work, emphasizing its focus on probability theory, including foundational concepts, distributions, and applications to legal decision-making processes.

Contribution

It introduces Poisson's pioneering application of probability theory to legal judgments and details his analysis of juror numbers and decision thresholds to reduce miscarriages of justice.

Findings

Analysis of probability principles and distributions

Poisson's calculation of optimal juror numbers

Insights into minimizing wrongful convictions

Abstract

In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named after Dirac; difference between objective and subjective probabilities; approximation of the Bernoulli theorem for rare events (but not yet the Poisson distribution); investigation of the significance of empirical discrepancies. Following Laplace, he actually attributed probability to applied mathematics. Poisson calculated the optimal number of jurors and of their majority for conviction/exoneration of the accused and in general studied the conditions enabling to minimize miscarriage of justice. He replaced guilty and innocent by convictable or not.